标题： 基于等稳坐标系的慢流形识别与计算 显示英文标题

标题： Identification and Computation of Slow Manifolds Using the Isostable Coordinate System

摘要： Koopman分析可用于以线性但通常为无限维算子的方式理解非线性动力系统的行为。 等相位坐标系关注最慢衰减的主要Koopman特征模式。 这项工作利用等相位坐标框架来识别具有固定点吸引子的动力系统的慢流形，这些流形定义为最快衰减的等相位坐标为零的表面。 与快慢时间尺度之间分离相关的数值挑战需要开发新的计算方法来识别这些慢流形。 开发了两种策略，这些策略近似从靠近固定点开始并在超出线性区域的慢流形上求解逆时间解。 应用于各种示例展示了这些方法的实用性及其在模型降阶方面的潜在用途。 显示英文摘要

摘要： Koopman analysis can be used to understand the dynamics of a nonlinear dynamical system in terms a linear, but generally infinite dimensional operator. The isostable coordinate system focuses on the slowest decaying principal Koopman eigenmodes. This work leverages the isostable coordinate framework in the identification of slow manifolds for dynamical systems with fixed point attractors, defined as surfaces for which the fastest decaying isostable coordinates are zero. Numerical challenges associated with separation between fast and slow timescales necessitate the development of new computational approaches to identify these slow manifolds. Two such strategies are developed which approximate backward-time solutions on the slow manifold starting near the fixed point and extending far beyond the linear regime. Application to a variety of examples illustrates the utility of these methods and their potential use for model order reduction purposes.